Bibliographic record
Abstract
The problem of estimating an unknown probability density function (pdf) is of fundamental importance in statistics and required for many statistical applications.In recent years, efficient nonparametric estimation has had greater focus on the problem of nonparametric regression, while the more challenging problem of density estimation has been given much less attention.In this thesis, we consider a class of kernel-type density estimators with Fejér-type kernels and theoretical smoothing parameters h n = (2γθ n )/ log n, where the parameter γ > 0 describes the class of underlying pdfs and 0 ≤ θ n < 1.In theory, the estimator under consideration dominates in L p , 1 ≤ p < ∞, all other known estimators from the literature in the locally asymptotic minimax (LAM) sense.We demonstrate via simulations that the estimator in question is good by comparing its performance to other fixed kernel estimators.The kernel-type estimator is also studied under empirical bandwidth selection methods such as the common cross-validation and the less-known method based on the Fourier analysis of kernel density estimators.The common L 2 -risk is used to assess the quality of estimation.The estimator of interest is then tried to real financial data for a risk measure that is widely used in many applications.The simulation results testify that, for a good choice of γ, the theoretical estimator under study provides very good finite sample performance compared to the other kernel estimators.The study also suggests that the bandwidth obtained by using the Fourier analysis techniques performs better than the one from cross-validation in most settings.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".